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8 Buffered and Isotonic SolutionsChapter ObjectivesAt the conclusion of this chapter the student should be able to:
1. Understand the common ion effect.2. Understand the relationship between pH, pKa, and ionization for weak acids and weak
bases.3. Apply the buffer equation, also known as the Henderson–Hasselbalch equation, for a
weak acid or base and its salt.4. Understand the relationship between activity coefficients and the buffer equation.5. Discuss the factors influencing the pH of buffer solutions.6. Understand the concept and be able to calculate buffer capacity.7. Describe the influence of concentration on buffer capacity.8. Discuss the relationship between buffer capacity and pH on tissue irritation.9. Describe the relationship between pH and solubility.10. Describe the concept of tonicity and its importance in pharmaceutical systems.11. Calculate solution tonicity and tonicity adjustments.
Buffers are compounds or mixtures of compounds that, by their presence in solution, resist changes in
pH upon the addition of small quantities of acid or alkali. The resistance to a change in pH is known
as buffer action. According to Roos and Borm,1 Koppel and Spiro published the first paper on buffer
action in 1914 and suggested a number of applications, which were later elaborated by Van Slyke.2
If a small amount of a strong acid or base is added to water or a solution of sodium chloride, the pH is
altered considerably; such systems have no buffer action.
The Buffer EquationCommon Ion Effect and the Buffer Equation for a Weak Acid and Its SaltThe pH of a buffer solution and the change in pH upon the addition of an acid or base can be calculated
by use of the buffer equation. This expression is developed by considering the effect of a salt on the
ionization of a weak acid when the salt and the acid have an ion in common.
Key ConceptWhat is a Buffer?A combination of a weak acid and its conjugate base (i.e., its salt) or a weak base and its conjugate acid acts as a buffer. If 1 mL of a 0.1 N HCl solution is added to 100 mL of pure water, the pH is reduced from 7 to 3. If the strong acid is added to a 0.01 M solution containing equal quantities of acetic acid and sodium acetate, the pH is changed only 0.09 pH units because the base Ac- ties up the hydrogen ions according to the reaction
If a strong base, sodium hydroxide, is added to the buffer mixture, acetic acid neutralizes the hydroxyl ions as follows:
For example, when sodium acetate is added to acetic acid, the dissociation constant for the weak acid,
is momentarily disturbed because the acetate ion supplied by the salt increases the [Ac-] term in the
numerator. To reestablish the constant Ka at 1.75 × 10-5, the hydrogen ion term in the numerator [H3O+]
is instantaneously decreased, with a corresponding increase in [HAc]. Therefore, the
constant Ka remains unaltered, and the equilibrium is shifted in the direction of the reactants.
Consequently, the ionization of acetic acid,
is repressed upon the addition of the common ion, Ac-. This is an example of the common ion effect.
The pH of the final solution is obtained by rearranging the equilibrium expression for acetic acid:
If the acid is weak and ionizes only slightly, the expression [HAc] may be considered to represent the
total concentration of acid, and it is written simply as [Acid]. In the slightly ionized acidic solution, the
acetate concentration [Ac-] can be considered as having come entirely from the salt, sodium acetate.
Because 1 mole of sodium acetate yields 1 mole of acetate ion, [Ac-] is equal to the total salt
concentration and is replaced by the term [Salt]. Hence, equation (8-5) is written as
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Equation (8-6) can be expressed in logarithmic form, with the signs reversed, as
from which is obtained an expression, known as the buffer equation or the Henderson–Hasselbalch
equation, for a weak acid and its salt:
The ratio [Acid]/[Salt] in equation (8-6) has been inverted by undertaking the logarithmic operations in
equation (8-7), and it appears in equation (8-8) as [Salt]/[Acid]. The term pKa, the negative logarithm
of Ka, is called the dissociation exponent.
The buffer equation is important in the preparation of buffered pharmaceutical solutions; it is satisfactory
for calculations within the pH range of 4 to 10.
Example 8-1pH CalculationWhat is the pH of 0.1 M acetic acid solution, pKa = 4.76? What is the pH after enough sodium acetate has been added to make the solution 0.1 M with respect to this salt?The pH of the acetic acid solution is calculated by use of the logarithmic form of equation (7-102):
The pH of the buffer solution containing acetic acid and sodium acetate is determined by use of the buffer equation (8-8):
It is seen from Example 8-1 that the pH of the acetic acid solution has been increased almost 2 pH units; that is, the acidity has been reduced to about 1/100 of its original value by the addition of an equal concentration of a salt with a common ion. This example bears out the statement regarding the repression of ionization upon the addition of a common ion.Sometimes it is desired to know the ratio of salt to acid in order to prepare a buffer of a definite pH. The following example demonstrates the calculation involved in such a problem.
Example 8-2pH and [Salt]/[Acid] RatioWhat is the molar ratio, [Salt]/[Acid], required to prepare an acetate buffer of pH 5.0? Also express the result in mole percent.
Therefore, the mole ratio of salt to acid is 1.74/1. Mole percent is mole fraction multiplied by 100. The mole fraction of salt in the salt–acid mixture is 1.74/(1 + 1.74) = 0.635, and in mole percent, the result is 63.5%.
The Buffer Equation for a Weak Base and Its SaltBuffer solutions are not ordinarily prepared from weak bases and their salts because of the volatility and
instability of the bases and because of the dependence of their pH on pKw, which is often affected by
temperature changes. Pharmaceutical solutions—for example, a solution of ephedrine base and
ephedrine hydrochloride—however, often contain combinations of weak bases and their salts.
The buffer equation for solutions of weak bases and the corresponding salts can be derived in a manner
analogous to that for the weak acid buffers. Accordingly,
and using the relationship [OH-] = Kw/[H3O+], the buffer equation is obtained
Example 8-3Using the Buffer EquationWhat is the pH of a solution containing 0.10 mole of ephedrine and 0.01 mole of ephedrine hydrochloride per liter of solution? Since the pKb of ephedrine is 4.64,
Activity Coefficients and the Buffer EquationA more exact treatment of buffers begins with the replacement of concentrations by activities in the
equilibrium of a weak acid:
The activity of each species is written as the activity coefficient multiplied by the molar concentration.
The activity coefficient of the undissociated acid, γHAc, is essentially 1 and may be dropped. Solving for
the hydrogen ion activity and pH, defined as -log aH3O+, yields the equations
From the Debye–Hückel expression for an aqueous solution of a univalent ion at 25°C having an ionic
strength not greater than about 0.1 or 0.2, we write
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and equation (8-13) then becomes
The general equation for buffers of polybasic acids is
where n is the stage of the ionization.
Example 8-4Activity Coefficients and BuffersA buffer contains 0.05 mole/liter of formic acid and 0.10 mole/liter of sodium formate. The pKa of formic acid is 3.75. The ionic strength of the solution is 0.10. Compute the pH (a) with and (b) without consideration of the activity coefficient correction.
Some Factors Influencing the pH of Buffer SolutionsThe addition of neutral salts to buffers changes the pH of the solution by altering the ionic strength, as
shown in equation (8-13). Changes in ionic strength and hence in the pH of a buffer solution can also be
brought about by dilution. The addition of water in moderate amounts, although not changing the pH,
may cause a small positive or negative deviation because it alters activity coefficients and because
water itself can act as a weak acid or base. Bates3 expressed this quantitatively in terms of a dilution
value, which is the change in pH on diluting the buffer solution to one half of its original strength. Some
dilution values for National Bureau of Standards buffers are given in Table 8-1. A positive dilution value
signifies that the pH rises with dilution and a negative value signifies that the pH decreases with dilution
of the buffer.
Table 8-1 Buffer Capacity of Solutions Containing Equimolar Amounts (0.1 M) of Acetic Acid And Sodium Acetate
Moles of NaOH AddedpH of SolutionBuffer Capacity, β
04.76
0.014.850.11
0.024.940.11
0.035.030.11
0.045.130.10
0.055.240.09
0.065.360.08
Temperature also influences buffers. Kolthoff and Tekelenburg4 determined the temperature coefficient
of pH, that is, the change in pH with temperature, for a large number of buffers. The pH of acetate
buffers was found to increase with temperature, whereas the pH of boric acid–sodium borate buffers
decreased with temperature. Although the temperature coefficient of acid buffers was relatively small,
the pH of most basic buffers was found to change more markedly with temperature, owing to Kw, which
appears in the equation of basic buffers and changes significantly with temperature. Bates3 referred to
several basic buffers that show only a small change of pH with temperature and can be used in the pH
range of 7 to 9. The temperature coefficients for the calomel electrode are given in the study by Bates.
Drugs as BuffersIt is important to recognize that solutions of drugs that are weak electrolytes also manifest buffer action.
Salicylic acid solution in a soft glass bottle is influenced by the alkalinity of the glass. It might be thought
at first that the reaction would result in an appreciable increase in pH; however, the sodium ions of the
soft glass combine with the salicylate ions to form sodium salicylate. Thus, there arises a solution of
salicylic acid and sodium salicylate—a buffer solution that resists the change in pH. Similarly, a solution
of ephedrine base manifests a natural buffer protection against reductions in pH. Should hydrochloric
acid be added to the solution, ephedrine hydrochloride is formed, and the buffer system of ephedrine
plus ephedrine hydrochloride will resist large changes in pH until the ephedrine is depleted by reaction
with the acid. Therefore, a drug in solution may often act as its own buffer over a definite pH range.
Such buffer action, however, is often too weak to counteract pH changes brought about by the carbon
dioxide of the air and the alkalinity of the bottle. Additional buffers are therefore frequently added to drug
solutions to maintain the system within a certain pH range. A quantitative measure of the efficiency or
capacity of a buffer to resist pH changes will be discussed in a later section.
pH IndicatorsIndicators may be considered as weak acids or weak bases that act like buffers and also exhibit color
changes as their degree of dissociation varies with pH. For example, methyl red shows its full alkaline
color, yellow, at a pH of about 6 and its full acid color, red, at about pH 4.
The dissociation of an acid indicator is given in simplified form as
The equilibrium expression is
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Table 8-2 Color, pH, and Indicator Constant, pKIn, of Some Common Indicators
IndicatorColor
pH RangepKIn AcidBase
Thymol blue (acid range)RedYellow1.2–2.81.5
Methyl violetBlueViolet1.5–3.2–
Methyl orangeRedYellow3.1–4.43.7
Bromcresol greenYellowBlue3.8–5.44.7
Methyl redRedYellow4.2–6.25.1
Bromcresol purpleYellowPurple5.2–6.86.3
Bromthymol blueYellowBlue6.0–7.67.0
Phenol redYellowRed6.8–8.47.9
Cresol redYellowRed7.2–8.88.3
Thymol blue (alkaline range)
YellowBlue8.0–9.68.9
PhenolphthaleinColorlessRed8.3–10.09.4
Alizarin yellowYellowLilac10.0–12.0
–
Indigo carmineBlueYellow11.6–14–
HIn is the un-ionized form of the indicator, which gives the acid color, and In- is the ionized form, which
produces the basic color. KIn is referred to as the indicator constant. If an acid is added to a solution of
the indicator, the hydrogen ion concentration term on the right-hand side of equation (8-16) is increased,
and the ionization is repressed by the common ion effect. The indicator is then predominantly in the
form of HIn, the acid color. If base is added, [H3O+] is reduced by reaction of the acid with the base,
reaction (8-16) proceeds to the right, yielding more ionized indicator In-, and the base color
predominates. Thus, the color of an indicator is a function of the pH of the solution. A number of
indicators with their useful pH ranges are listed in Table 8-2.
The equilibrium expression (8-16) can be treated in a manner similar to that for a buffer consisting of a
weak acid and its salt or conjugate base. Hence
and because [HIn] represents the acid color of the indicator and the conjugate base [In-] represents the
basic color, these terms can be replaced by the concentration expressions [Acid] and [Base]. The
formula for pH as derived from equation (8-18) becomes
Example 8-5Calculate pH
An indicator, methyl red, is present in its ionic form In-, in a concentration of 3.20 × 103 M and in its molecular form, HIn, in an aqueous solution at 25°C in a concentration of 6.78 × 103 M. From Table 8-2 a pKIn of 5.1 is observed for methyl red. What is the pH of this solution? We have
Just as a buffer shows its greatest efficiency when pH = pKa, an indicator exhibits its middle tint when
[Base]/[Acid] = 1 and pH = pKIn. The most efficient indicator range, corresponding to the effective buffer
interval, is about 2 pH units, that is, pKIn ± 1. The reason for the width of this color range can be
explained as follows. It is known from experience that one cannot discern a change from the acid color
to the salt or conjugate base color until the ratio of [Base] to [Acid] is about 1 to 10. That is, there must
be at least 1 part of the basic color to 10 parts of the acid color before the eye can discern a change in
color from acid to alkaline. The pH value at which this change is perceived is given by the equation
Conversely, the eye cannot discern a change from the alkaline to the acid color until the ratio of [Base]
to [Acid] is about 10 to 1, or
Therefore, when base is added to a solution of a buffer in its acid form, the eye first visualizes a change
in color at pKIn - 1, and the color ceases to change any further at pKIn + 1. The effective range of the
indicator between its full acid and full basic color can thus be expressed as
Chemical indicators are typically compounds with chromophores that can be detected in the visible
range and change color in response to a solution's pH. Most chemicals used as indicators respond only
to a narrow pH range. Several indicators can be combined to yield so-called universal indicators just as
buffers can be mixed to cover a wide pH range. A universal indicator is a pH indicator that displays
different colors as the pH transitions from pH 1 to 12. A typical universal indicator will display a color
range from red to purple8
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For example, a strong acid (pH 0–3) may display as red in color, an acid (pH 3–6) as orange–yellow,
neutral pH (pH 7) as green, alkaline pH (pH 8–11) as blue, and purple for strong alkaline pH (pH 11–
14).
The colorimetric method for the determination of pH is probably less accurate and less convenient but is
also less expensive than electrometric methods and it can be used in the determination of the pH of
aqueous solutions that are not colored or turbid. This is particularly useful for the study of acid–base
reactions in nonaqueous solutions. A note of caution should be added regarding the colorimetric
method. Because indicators themselves are acids (or bases), their addition to unbuffered solutions
whose pH is to be determined will change the pH of the solution. The colorimetric method is therefore
not applicable to the determination of the pH of sodium chloride solution or similar unbuffered
pharmaceutical preparations unless special precautions are taken in the measurement. Some medicinal
solutions and pharmaceutical vehicles, however, to which no buffers have been added are buffered by
the presence of the drug itself and can withstand the addition of an indicator without a significant change
in pH. Errors in the result can also be introduced by the presence of salts and proteins, and these errors
must be determined for each indicator over the range involved.
Recently, Kong et al.5 reported on a rapid method for determining pKa based on spectrophotometric
titration using a universal pH indicator. Historically, potentiometric titration, which typically uses pH
electrodes, has been the most commonly used method for determining pKa values. This method takes
time and requires the daily calibration of the pH electrode. Spectrophotometric titration has the
advantage that less sample is required, it is not affected by CO2 interference, and it can provide
multiwavelength absorbance information. The method can be applied only to compounds with
chromophores placed close to the titratable groups. The indicator spectra can then be used to calculate
the pH value of a solution from the pKa values, concentration, and molar extinction coefficients of the
indicator species. In contrast to pH electrodes, chemical indicators respond rapidly and do not require
frequent calibration.
Buffer CapacityThus far it has been stated that a buffer counteracts the change in pH of a solution upon the addition of
a strong acid, a strong base, or other agents that tend to alter the hydrogen ion concentration.
Furthermore, it has been shown in a rather qualitative manner how combinations of weak acids and
weak bases together with their salts manifest this buffer action. The resistance to changes of pH now
remains to be discussed in a more quantitative way.
The magnitude of the resistance of a buffer to pH changes is referred to as the buffer capacity, β. It is
also known as buffer efficiency, buffer index, and buffer value. Koppel and Spiro1 and Van
Slyke2 introduced the concept of buffer capacity and defined it as the ratio of the increment of strong
base (or acid) to the small change in pH brought about by this addition. For the present discussion, the
approximate formula
can be used, in which delta, Δ, has its usual meaning, a finite change, and ΔB is the small increment in
gram equivalents (g Eq)/liter of strong base added to the buffer solution to produce a pH change of Δ
pH. According to equation (8-23), the buffer capacity of a solution has a value of 1 when the addition of
1 g Eq of strong base (or acid) to 1 liter of the buffer solution results in a change of 1 pH unit. The
significance of this index will be appreciated better when it is applied to the calculation of the capacity of
a buffer solution.
Approximate Calculation of Buffer CapacityConsider an acetate buffer containing 0.1 mole each of acetic acid and sodium acetate in 1 liter of
solution. To this are added 0.01-mole portions of sodium hydroxide. When the first increment of sodium
hydroxide is added, the concentration of sodium acetate, the [Salt] term in the buffer equation, increases
by 0.01 mole/liter and the acetic acid concentration, [Acid], decreases proportionately because each
increment of base converts 0.01 mole of acetic acid into 0.01 mole of sodium acetate according to the
reaction
The changes in concentration of the salt and the acid by the addition of a base are represented in the
buffer equation (8-8) by using the modified form
Before the addition of the first portion of sodium hydroxide, the pH of the buffer solution is
The results of the continual addition of sodium hydroxide are shown in Table 8-1. The student should
verify the pH values and buffer capacities by the use of equations (8-25) and (8-23), respectively.
As can be seen from Table 8-1, the buffer capacity is not a fixed value for a given buffer system but
instead depends on the amount of base added. The buffer capacity changes as the ratio
log([Salt]/[Acid]) increases with added base. With the addition of more sodium hydroxide, the buffer
capacity decreases rapidly, and, when sufficient base has been added to convert the acid completely
into sodium ions and acetate ions, the solution no longer possesses an acid reserve. The buffer has its
greatest capacity before any base is added, where [Salt]/[Acid] = 1, and, therefore, according to
equation (8-8), pH = pKa. The buffer capacity is also influenced
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by an increase in the total concentration of the buffer constituents because, obviously, a great
concentration of salt and acid provides a greater alkaline and acid reserve. The influence of
concentration on buffer capacity is treated following the discussion of Van Slyke's equation.
A More Exact Equation for Buffer CapacityThe buffer capacity calculated from equation (8-23) is only approximate. It gives the average buffer
capacity over the increment of base added. Koppel and Spiro1 and Van Slyke2 developed a more exact
equation,
where C is the total buffer concentration, that is, the sum of the molar concentrations of the acid and the
salt. Equation (8-27) permits one to compute the buffer capacity at any hydrogen ion concentration—for
example, at the point where no acid or base has been added to the buffer.
Example 8-6Calculating Buffer CapacityAt a hydrogen ion concentration of 1.75 × 10-5 (pH = 4.76), what is the capacity of a buffer containing 0.10 mole each of acetic acid and sodium acetate per liter of solution? The total concentration, C = [Acid] + [Salt], is 0.20 mole/liter, and the dissociation constant is 1.75 × 10-
5. We have
Example 8-7Buffer Capacity and pHPrepare a buffer solution of pH 5.00 having a capacity of 0.02. The steps in the solution of the problem are as follows:
a. Choose a weak acid having a pKa close to the pH desired. Acetic acid, pKa = 4.76, is suitable in this case.
b. The ratio of salt and acid required to produce a pH of 5.00 was found in Example 8-2 to be [Salt]/[Acid] = 1.74/1.
c. Use the buffer capacity equation (8-27) to obtain the total buffer concentration, C = [Salt] + [Acid]:
d. Finally from (b), [Salt] = 1.74 × [Acid], and from (c),
Therefore,
and
The Influence of Concentration on Buffer CapacityThe buffer capacity is affected not only by the [Salt]/[Acid] ratio but also by the total concentrations of
acid and salt. As shown in Table 8-1, when 0.01 mole of base is added to a 0.1 molar acetate buffer, the
pH increases from 4.76 to 4.85, for a ΔpH of 0.09.
If the concentration of acetic acid and sodium acetate is raised to 1 M, the pH of the original buffer
solution remains at about 4.76, but now, upon the addition of 0.01 mole of base, it becomes 4.77, for a
ΔpH of only 0.01. The calculation, disregarding activity coefficients, is
Therefore, an increase in the concentration of the buffer components results in a greater buffer capacity
or efficiency. This conclusion is also evident in equation (8-27), where an increase in the total buffer
concentration, C = [Salt] + [Acid], obviously results in a greater value of β.
Maximum Buffer CapacityAn equation expressing the maximum buffer capacity can be derived from the buffer capacity formula of
Koppel and Spiro1 and Van Slyke,2 equation (8-27). The maximum buffer capacity occurs where pH =
pKa, or, in equivalent terms, where [H3O+] = Ka. Substituting [H3O+] for Ka in both the numerator and the
denominator of equation (8-27) gives
where C is the total buffer concentration.
Example 8-8Maximum Buffer CapacityWhat is the maximum buffer capacity of an acetate buffer with a total concentration of 0.020 mole/liter? We have
Key ConceptBuffer CapacityThe buffer capacity depends on (a) the value of the ratio [Salt]/[Acid], increasing as the ratio approaches unity, and (b) the magnitude of the individual concentrations of the buffer components, the buffer becoming more efficient as the salt and acid concentrations are increased.
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Neutralization Curves and Buffer CapacityA further understanding of buffer capacity can be obtained by considering the titration curves of strong
and weak acids when they are mixed with increasing quantities of alkali. The reaction of an equivalent of
an acid with an equivalent of a base is called neutralization; it can be expressed according to the
method of Brönsted and Lowry. The neutralization of a strong acid by a strong base and a weak acid by
a strong base is written in the form
where (H3O+)(Cl-) is the hydrated form of HCl in water. The neutralization of a strong acid by a strong
base simply involves a reaction between hydronium and hydroxyl ions and is usually written as
Because (Cl-) and (Na+) appear on both sides of the reaction equation just given, they may be
disregarded without influencing the result. The reaction between the strong acid and the strong base
proceeds almost to completion; however, the weak acid–strong base reaction is incomplete because
Ac- reacts in part with water, that is, it hydrolyzes to regenerate the free acid.
The neutralization of 10 mL of 0.1 N HCl (curve I) and 10 mL of 0.1 N acetic acid (curve II) by 0.1 N
NaOH is shown in Figure 8-1. The plot of pH versus milliliters of NaOH added produces the titration
curve. It is computed as follows for HCl. Before the first increment of NaOH is added, the hydrogen ion
concentration of the 0.1 N solution of HCl is 10-1 mole/liter, and the pH is 1, disregarding activities and
assuming HCl to be completely ionized. The addition of 5 mL of 0.1 N NaOH neutralizes 5 mL of 0.1 N
HCl, leaving 5 mL of the original HCl in 10 + 5 = 15 mL of solution, or [H3O+] = 5/15 × 0.1 = 3.3 × 10-
2 mole/liter, and the pH is 1.48. When 10 mL of base has been added, all the HCl is converted to NaCl,
and the pH, disregarding the difference between activity and concentration resulting from the ionic
strength of the NaCl solution, is 7. This is known as the equivalence point of the titration. Curve I
in Figure 8-1 results from plotting such data. It is seen that the pH does not change markedly until nearly
all the HCl is neutralized. Hence, a solution of a strong acid has a high buffer capacity below a pH of 2.
Likewise, a strong base has a high buffer capacity above a pH of 12.
Fig. 8-1. Neutralization of a strong acid and a weak acid by a strong base.
The buffer capacity equations considered thus far have pertained exclusively to mixtures of weak
electrolytes and their salts. The buffer capacity of a solution of a strong acid was shown by Van Slyke to
be directly proportional to the hydrogen ion concentration, or
The buffer capacity of a solution of a strong base is similarly proportional to the hydroxyl ion
concentration,
The total buffer capacity of a water solution of a strong acid or base at any pH is the sum of the
separate capacities just given, equations (8-31) and (8-32), or
Example 8-9Calculate Buffer CapacityWhat is the buffer capacity of a solution of hydrochloric acid having a hydrogen ion concentration of 10-2 mole/liter?The hydroxyl ion concentration of such a solution is 10-12, and the total buffer capacity is
The OH- concentration is obviously so low in this case that it may be neglected in the calculation.
Three equations are normally used to obtain the data for the titration curve of a weak acid (curve II
of Fig. 8-1), although a single equation that is somewhat complicated can be used. Suppose that
increments of 0.1 N NaOH are added to 10 mL of a 0.1 N HAc solution.
a. The pH of the solution before any NaOH has been added is obtained from the equation for a
weak acid,
b. At the equivalence point, where the acid has been converted completely into sodium ions and
acetate ions, the
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pH is computed from the equation for a salt of a weak acid and strong base in log form:
The concentration of the acid is given in the last term of this equation as 0.05 because the
solution has been reduced to half its original value by mixing it with an equal volume of base at
the equivalence point.
c. Between these points on the neutralization curve, the increments of NaOH convert some of the
acid to its conjugate base Ac- to form a buffer mixture, and the pH of the system is calculated
from the buffer equation. When 5 mL of base is added, the equivalent of 5 mL of 0.1 N acid
remains and 5 mL of 0.1 N Ac- is formed, and using the Henderson–Hasselbalch equation, we
obtain
The slope of the curve is a minimum and the buffer capacity is greatest at this point, where the
solution shows the smallest pH change per g Eq of base added. The buffer capacity of a
solution is the reciprocal of the slope of the curve at a point corresponding to the composition
of the buffer solution. As seen inFigure 8-1, the slope of the line is a minimum, and the buffer
capacity is greatest at half-neutralization, where pH = pKa.
The titration curve for a tribasic acid such as H3PO4 consists of three stages, as shown in Figure 8-2.
These can be considered as being produced by three separate acids (H3PO4, pK1 = 2.21; H2PO4-, pK2 =
7.21; and HPO42-, pK3 = 12.67) whose strengths are sufficiently different so that their curves do not
overlap. The curves can be plotted by using the buffer equation and their ends joined by smooth lines to
produce the continuous curve of Figure 8-2.
Fig. 8-2. Neutralization of a tribasic acid.
Fig. 8-3. Neutralization curve for a universal buffer. (From H. T. Britton, Hydrogen Ions, Vol. I, Van Nostrand, New York, 1956, p. 368.)
A mixture of weak acids whose pKa values are sufficiently alike (differing by no more than about 2 pH
units) so that their buffer regions overlap can be used as auniversal buffer over a wide range of pH
values. A buffer of this type was introduced by Britton and Robinson.6 The three stages of citric acid,
pK1 = 3.15, pK2 = 4.78, and pK3 = 6.40, are sufficiently close to provide overlapping of neutralization
curves and efficient buffering over this range. Adding Na2HPO4, whose conjugate acid, H2PO4-, has a
pK2 of 7.2, diethylbarbituric acid, pK1 = 7.91, and boric acid, pK1 = 9.24, provides a universal buffer that
covers the pH range of about 2.4 to 12. The neutralization curve for the universal buffer mixture is linear
between pH 4 and 8, as seen in Figure 8-3, because the successive dissociation constants differ by only
a small value.
A titration curve depends on the ratio of the successive dissociation constants. Theoretically, when
one K is equal to or less than 16 times the previous K, that is, when successive pKs do not differ by
greater than 1.2 units, the second ionization begins well before the first is completed, and the titration
curve is a straight line with no inflection points. Actually, the inflection is not noticeable until one K is
about 50 to 100 times that of the previous K value.
The buffer capacity of several acid–salt mixtures is plotted against pH in Figure 8-4. A buffer solution is
useful within a range of about ±1 pH unit about the pKa of its acid, where the buffer capacity is roughly
greater than 0.01 or 0.02, as observed in Figure 8-4. Accordingly, the acetate buffer should be effective
over a pH range of about 3.8 to 5.8, and the borate buffer should be effective over a range of 8.2 to
10.2. In each case, the greatest capacity occurs where [Salt]/[Acid] = 1 and pH = pKa. Because of
interionic effects, buffer capacities do not in general exceed a value of 0.2. The buffer capacity of a
solution of the strong acid HCl becomes marked below a pH of 2, and the buffer capacity of a strong
base NaOH becomes significant above a pH of 12.
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Fig. 8-4. The buffer capacity of several buffer systems as a function of pH. (Modified from R. G. Bates, Electrometric pH Determinations, Wiley, New York, 1954.)
The buffer capacity of a combination of buffers whose pKa values overlap to produce a universal buffer
is plotted in Figure 8-5. It is seen that the total buffer capacity Σβ is the sum of the β values of the
individual buffers. In this figure, it is assumed that the maximum βs of all buffers in the series are
identical.
Buffers in Pharmaceutical and Biologic SystemsIn Vivo Biologic Buffer SystemsBlood is maintained at a pH of about 7.4 by the so-called primary buffers in the plasma and the
secondary buffers in the erythrocytes. The plasma contains carbonic acid/bicarbonate and acid/alkali
sodium salts of phosphoric acid as buffers. Plasma proteins, which behave as acids in blood, can
combine with bases and so act as buffers. In the erythrocytes, the two buffer systems consist of
hemoglobin/oxyhemoglobin and acid/alkali potassium salts of phosphoric acid.
The dissociation exponent pK1 for the first ionization stage of carbonic acid in the plasma at body
temperature and an ionic strength of 0.16 is about 6.1. The buffer equation for the carbonic
acid/bicarbonate buffer of the blood is
Fig. 8-5. The total buffer capacity of a universal buffer as a function of a pH. (From I. M. Kolthoff and C. Rosenblum, Acid–Base Indicators, Macmillan, New York, 1937, p. 29.)
where [H2CO3] represents the concentration of CO2 present as H2CO3 dissolved in the blood. At a pH of
7.4, the ratio of bicarbonate to carbonic acid in normal blood plasma is
or
This result checks with experimental findings because the actual concentrations of bicarbonate and
carbonic acid in the plasma are about 0.025 M and 0.00125 M, respectively.
The buffer capacity of the blood in the physiologic range pH 7.0 to 7.8 is obtained as follows. According
to Peters and Van Slyke,7 the buffer capacity of the blood owing to hemoglobin and other constituents,
exclusive of bicarbonate, is about 0.025 g equivalents per liter per pH unit. The pH of the bicarbonate
buffer in the blood (i.e., pH 7.4) is rather far removed from the pH (6.1) where it exhibits maximum buffer
capacity; therefore, the bicarbonate's buffer action is relatively small with respect to that of the other
blood constituents. According to the calculation just given, the ratio [NaHCO3]/[H2CO3] is 20:1 at pH 7.4.
Using equation (8-27), we find the buffer capacity for the bicarbonate system (K1 = 4 × 10-7) at a pH of
7.4 ([H3O+] = 4 × 10-8) to be roughly 0.003. Therefore, the total buffer capacity of the blood in the
physiologic range, the sum of the capacities of the various constituents, is 0.025 + 0.003 = 0.028.
Salenius8 reported a value of 0.0318 ± 0.0035 for whole blood, whereas Ellison et al.9 obtained a buffer
capacity of about 0.039 g equivalents per liter per pH unit for whole blood, of which 0.031 was
contributed by the cells and 0.008 by the plasma.
It is usually life-threatening for the pH of the blood to go below 6.9 or above 7.8. The pH of the blood in
diabetic coma is as low as about 6.8.
Lacrimal fluid, or tears, have been found to have a great degree of buffer capacity, allowing a dilution of
1:15 with neutral distilled water before an alteration of pH is noticed.10 In the terminology of
Bates,11 this would be referred to today as dilution value rather than buffer capacity. The pH of tears is
about 7.4, with a range of 7 to 8 or slightly higher. It is generally thought that eye drops within a pH
range of 4 to 10 will not harm the cornea.12 However, discomfort and a flow of tears will occur below pH
6.6 and above pH 9.0.12 Pure conjunctival fluid is probably more acidic than the tear fluid commonly
used in pH measurements. This is because pH increases rapidly when the sample is removed for
analysis because of the loss of CO2 from the tear fluid.
UrineThe 24-hr urine collection of a normal adult has a pH averaging about 6.0 units; it may be as low as 4.5
or as high as 7.8. When the pH of the urine is below normal values, hydrogen ions are excreted by the
kidneys. Conversely, when the
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urine is above pH 7.4, hydrogen ions are retained by action of the kidneys in order to return the pH to its
normal range of values.
Pharmaceutical BuffersBuffer solutions are used frequently in pharmaceutical practice, particularly in the formulation of
ophthalmic solutions. They also find application in the colorimetric determination of pH and for research
studies in which pH must be held constant.
Gifford13 suggested two stock solutions, one containing boric acid and the other monohydrated sodium
carbonate, which, when mixed in various proportions, yield buffer solutions with pH values from about 5
to 9.
Sörensen14 proposed a mixture of the salts of sodium phosphate for buffer solutions of pH 6 to 8.
Sodium chloride is added to each buffer mixture to make it isotonic with body fluids.
A buffer system suggested by Palitzsch15 and modified by Hind and Goyan16 consists of boric acid,
sodium borate, and sufficient sodium chloride to make the mixtures isotonic. It is used for ophthalmic
solutions in the pH range of 7 to 9.
The buffers of Clark and Lubs,17 based on the original pH scale of Sörensen, have been redetermined
at 25°C by Bower and Bates18 so as to conform to the present definition of pH. Between pH 3 and 11,
the older values were about 0.04 unit lower than the values now assigned, and at the ends of the scale,
the differences were greater. The original values were determined at 20°C, whereas most experiments
today are performed at 25°C.
The Clark–Lubs mixtures and their corresponding pH ranges are as follows:
a. HCl and KCl, pH 1.2 to 2.2
b. HCl and potassium hydrogen phthalate, pH 2.2 to 4.0
c. NaOH and potassium hydrogen phthalate, pH 4.2 to 5.8
d. NaOH and KH2PO4, pH 5.8 to 8.0
e. H3BO3, NaOH, and KCl, pH 8.0 to 10.0
With regard to mixture (a), consisting of HCl and KCl and used for the pH range from 1.0 to 2.2, it will be
recalled from the discussion of the neutralization curve I inFigure 8-1 that HCl alone has considerable
buffer efficiency below pH 2. KCl is a neutral salt and is added to adjust the ionic strength of the buffer
solutions to a constant value of 0.10; the pH calculated from the equation -log aH+ = -log (y ± c)
corresponds closely to the experimentally determined pH. The role of the KCl in the Clark–Lubs buffer is
sometimes erroneously interpreted as that of a salt of the buffer acid, HCl, corresponding to the part
played by sodium acetate as the salt of the weak buffer acid, HAc. Potassium chloride is added to (e),
the borate buffer, to produce an ionic strength comparable to that of (d), the phosphate buffer, where the
pH of the two buffer series overlaps.
Key ConceptPhosphate Buffered SalineThere are several variations in the formula for preparing PBS. Two common examples follow:Formula One: Take 8 g NaCl, 0.2 g KCl, 1.44 g Na2HPO4, and 0.24 g KH2PO4 in 800 mL distilled water. Adjust pH to 7.4 using HCl. Add sufficient (qs ad) distilled water to achieve 1 liter.Formula Two: Another variant of PBS. This one is designated as “10X PBS (0.1 M PBS, pH 7.2)” since it is much more concentrated than PBS and the pH is not yet adjusted to pH 7.4. Take 90 g NaCl, 10.9 g Na2HPO4, and 3.2 g NaH2PO4 in 1000 mL distilled water. Dilute 1:10 using distilled water and adjust pH as necessary.
Many buffers are available today. One of the most common biological buffers is phosphate buffered
saline (PBS). Phosphate buffered saline contains sodium chloride (NaCl) and dibasic sodium phosphate
(Na2PO4). It may also contain potassium chloride (KCl), monobasic potassium phosphate (KH2PO4),
calcium chloride (CaCl2), and magnesium sulfate (MgSO4).
General Procedures for Preparing Pharmaceutical Buffer SolutionsThe pharmacist may be called upon at times to prepare buffer systems for which the formulas do not
appear in the literature. The following steps should be helpful in the development of a new buffer.
a. Select a weak acid having a pKa approximately equal to the pH at which the buffer is to be
used. This will ensure maximum buffer capacity.
b. From the buffer equation, calculate the ratio of salt and weak acid required to obtain the
desired pH. The buffer equation is satisfactory for approximate calculations within the pH range
of 4 to 10.
c. Consider the individual concentrations of the buffer salt and acid needed to obtain a suitable
buffer capacity. A concentration of 0.05 to 0.5 M is usually sufficient, and a buffer capacity of
0.01 to 0.1 is generally adequate.
d. Other factors of some importance in the choice of a pharmaceutical buffer include availability of
chemicals, sterility of the final solution, stability of the drug and buffer on aging, cost of
materials, and freedom from toxicity. For example, a borate buffer, because of its toxic effects,
certainly cannot be used to stabilize a solution to be administered orally or parenterally.
e. Finally, determine the pH and buffer capacity of the completed buffered solution using a
reliable pH meter. In some cases, sufficient accuracy is obtained by the use of
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pH papers. Particularly when the electrolyte concentration is high, it may be found that the pH
calculated by use of the buffer equation is somewhat different from the experimental value.
This is to be expected when activity coefficients are not taken into account, and it emphasizes
the necessity for carrying out the actual determination.
Influence of Buffer Capacity and pH on Tissue IrritationFriedenwald et al.18 claimed that the pH of solutions for introduction into the eye may vary from 4.5 to
11.5 without marked pain or damage. This statement evidently would be true only if the buffer capacity
were kept low. Martin and Mims19 found that Sörensen's phosphate buffer produced irritation in the
eyes of a number of individuals when used outside the narrow pH range of 6.5 to 8, whereas a boric
acid solution of pH 5 produced no discomfort in the eyes of the same individuals. Martin and Mims
concluded that a pH range of nonirritation cannot be established absolutely but instead depends upon
the buffer employed. In light of the previous discussion, this apparent anomaly can be explained partly
in terms of the low buffer capacity of boric acid as compared with that of the phosphate buffer and partly
to the difference of the physiologic response to various ion species.
Riegelman and Vaughn20 assumed that the acid-neutralizing power of tears when 0.1 mL of a 1%
solution of a drug is instilled into the eye is roughly equivalent to 10 µL of a 0.01 N strong base. They
pointed out that although in a few cases, irritation of the eye may result from the presence of the free
base form of a drug at the physiologic pH, it is more often due to the acidity of the eye solution. For
example, because only one carboxyl group of tartaric acid is neutralized by epinephrine base in
epinephrine bitartrate, a 0.06 M solution of the drug has a pH of about 3.5. The prolonged pain resulting
from instilling two drops of this solution into the eye is presumably due to the unneutralized acid of the
bitartrate, which requires 10 times the amount of tears to restore the normal pH of the eye as compared
with the result following two drops of epinephrine hydrochloride. Solutions of pilocarpine salts also
possess sufficient buffer capacity to cause pain or irritation owing to their acid reaction when instilled
into the eye.
Parenteral solutions for injection into the blood are usually not buffered, or they are buffered to a low
capacity so that the buffers of the blood may readily bring them within the physiologic pH range. If the
drugs are to be injected only in small quantities and at a slow rate, their solutions can be buffered
weakly to maintain approximate neutrality.
According to Mason,21 following oral administration, aspirin is absorbed more rapidly in systems
buffered at low buffer capacity than in systems containing no buffer or in highly buffered preparations.
Thus, the buffer capacity of the buffer should be optimized to produce rapid absorption and minimal
gastric irritation of orally administered aspirin.
Key ConceptParenteral SolutionsSolutions to be applied to tissues or administered parenterally are liable to cause irritation if their pH is greatly different from the normal pH of the relevant body fluid. Consequently, the pharmacist must consider this point when formulating ophthalmic solutions, parenteral products, and fluids to be applied to abraded surfaces. Of possible greater significance than the actual pH of the solution is its buffer capacity and the volume to be used in relation to the volume of body fluid with which the buffered solution will come in contact. The buffer capacity of the body fluid should also be considered. Tissue irritation, due to large pH differences between the solution being administered and the physiologic environment in which it is used, will be minimal (a) the lower is the buffer capacity of the solution, (b) the smaller is the volume used for a given concentration, and (c) the larger are the volume and buffer capacity of the physiologic fluid.
In addition to the adjustment of tonicity and pH for ophthalmic preparations, similar requirements are
demanded for nasal delivery of drugs. Conventionally, the nasal route has been used for delivery of
drugs for treatment of local diseases such as nasal allergy, nasal congestion, and nasal
infections.22 The nasal route can be exploited for the systemic delivery of drugs such as small
molecular weight polar drugs, peptides and proteins that are not easily administered via other routes
than by injection, or where a rapid onset of action is required. Examples include buserelin,
desmopressin, and nafarelin.
Stability versus Optimum Therapeutic ResponseFor the sake of completeness, some mention must be made at this point of the effect of buffer capacity
and pH on the stability and therapeutic response of the drug being used in solution.
As will be discussed later, the undissociated form of a weakly acidic or basic drug often has a higher
therapeutic activity than that of the dissociated salt form. This is because the former is lipid soluble and
can penetrate body membranes readily, whereas the ionic form, not being lipid soluble, can penetrate
membranes only with greater difficulty. Thus, Swan and White23 and Cogan and Kinsey24 observed an
increase in therapeutic response of weakly basic alkaloids (used as ophthalmic drugs) as the pH of the
solution, and hence concentration of the undissociated base, was increased. At a pH of about 4, these
drugs are predominantly in the ionic form, and penetration is slow or insignificant. When the tears bring
the pH to about 7.4, the drugs may exist to a significant degree in the form of the free base, depending
on the dissociation constant of the drug.
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Example 8-10Mole Percent of Free BaseThe pKb of pilocarpine is 7.15 at 25°C. Compute the mole percent of free base present at 25°C and at a pH of 7.4. We have
Hind and Goyan25 pointed out that the pH for maximum stability of a drug for ophthalmic use may be far
below that of the optimum physiologic effect. Under such conditions, the solution of the drug can be
buffered at a low buffer capacity and at a pH that is a compromise between that of optimum stability and
the pH for maximum therapeutic action. The buffer is adequate to prevent changes in pH due to the
alkalinity of the glass or acidity of CO2 from dissolved air. Yet, when the solution is instilled in the eye,
the tears participate in the gradual neutralization of the solution; conversion of the drug occurs from the
physiologically inactive form to the undissociated base. The base can then readily penetrate the lipoidal
membrane. As the base is absorbed at the pH of the eye, more of the salt is converted into base to
preserve the constancy of pKb; hence, the alkaloidal drug is gradually absorbed.
pH and Solubility
Since the relationship between pH and the solubility of weak electrolytes is treated elsewhere in the
book, it is only necessary to point out briefly the influence of buffering on the solubility of an alkaloidal
base. At a low pH, a base is predominantly in the ionic form, which is usually very soluble in aqueous
media. As the pH is raised, more undissociated base is formed, as calculated by the method illustrated
in Example 8-10. When the amount of base exceeds the limited water solubility of this form, free base
precipitates from solution. Therefore, the solution should be buffered at a sufficiently low pH so that the
concentration of alkaloidal base in equilibrium with its salt is calculated to be less than the solubility of
the free base at the storage temperature. Stabilization against precipitation can thus be maintained.
Buffered Isotonic SolutionsReference has already been made to in vivo buffer systems, such as blood and lacrimal fluid, and the
desirability for buffering pharmaceutical solutions under certain conditions. In addition to carrying out pH
adjustment, pharmaceutical solutions that are meant for application to delicate membranes of the body
should also be adjusted to approximately the same osmotic pressure as that of the body fluids. Isotonic
solutions cause no swelling or contraction of the tissues with which they come in contact and produce
no discomfort when instilled in the eye, nasal tract, blood, or other body tissues. Isotonic sodium
chloride is a familiar pharmaceutical example of such a preparation.
The need to achieve isotonic conditions with solutions to be applied to delicate membranes is
dramatically illustrated by mixing a small quantity of blood with aqueous sodium chloride solutions of
varying tonicity. For example, if a small quantity of blood, defibrinated to prevent clotting, is mixed with a
solution containing 0.9 g of NaCl per 100 mL, the cells retain their normal size. The solution has
essentially the same salt concentration and hence the same osmotic pressure as the red blood cell
contents and is said to be isotonic with blood. If the red blood cells are suspended in a 2.0% NaCl
solution, the water within the cells passes through the cell membrane in an attempt to dilute the
surrounding salt solution until the salt concentrations on both sides of the erythrocyte membrane are
identical. This outward passage of water causes the cells to shrink and become wrinkled or crenated.
The salt solution in this instance is said to be hypertonic with respect to the blood cell contents. Finally,
if the blood is mixed with 0.2% NaCl solution or with distilled water, water enters the blood cells, causing
them to swell and finally burst, with the liberation of hemoglobin. This phenomenon is known
as hemolysis, and the weak salt solution or water is said to be hypotonic with respect to the blood.
The student should appreciate that the red blood cell membrane is not impermeable to all drugs; that is,
it is not a perfect semipermeable membrane. Thus, it will permit the passage of not only water
molecules but also solutes such as urea, ammonium chloride, alcohol, and boric acid.26 A 2.0%
solution of boric acid has the same osmotic pressure as the blood cell contents when determined by the
freezing point method and is therefore said to be isosmotic with blood. The molecules of boric acid pass
freely through the erythrocyte membrane, however, regardless of concentration. As a result, this
solution acts essentially as water when in contact with blood cells. Because it is extremely hypotonic
with respect to the blood, boric acid solution brings about rapid hemolysis. Therefore, a solution
containing a quantity of drug calculated to be isosmotic with blood is isotonic only when
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the blood cells are impermeable to the solute molecules and permeable to the solvent, water. It is
interesting to note that the mucous lining of the eye acts as a true semipermeable membrane to boric
acid in solution. Accordingly, a 2.0% boric acid solution serves as an isotonic ophthalmic preparation.
Key ConceptTonicity
Osmolality and osmolarity are colligative properties that measure the concentration of the solutes independently of their ability to cross a cell membrane. Tonicity is the concentration of only the solutes that cannot cross the membrane since these solutes exert an osmotic pressure on that membrane. Tonicity is not the difference between the two osmolarities on opposing sides of the membrane. A solution might be hypertonic, isotonic, or hypotonic relative to another solution. For example, the relative tonicity of blood is defined in reference to that of the red blood cell (RBC) cytosol tonicity. As such, a hypertonic solution contains a higher concentration of impermeable solutes than the cytosol of the RBC; there is a net flow of fluid out of the RBC and it shrinks (Panel A). The concentration of impermeable solutes in the solution and cytosol are equal and the RBCs remain unchanged, so there is no net fluid flow (Panel B). A hypotonic solution contains a lesser concentration of such solutes than the RBC cytosol and fluid flows into the cells where they swell and potentially burst (Panel C). In short, a solution containing a quantity of drug calculated to be isosmotic with blood is isotonic only when the blood cells are impermeable to the solute (drug) molecules and permeable to the solvent, water.
To overcome this difficulty, Husa27 suggested that the term isotonic should be restricted to solutions
having equal osmotic pressures with respect to a particular membrane. Goyan and Reck28 felt that,
rather than restricting the use of the term in this manner, a new term should be introduced that is
defined on the basis of the sodium chloride concentration. These workers defined the term isotonicity
value as the concentration of an aqueous NaCl solution having the same colligative properties as the
solution in question. Although all solutions having an isotonicity value of 0.9 g of NaCl per 100 mL of
solution need not necessarily be isotonic with respect to the living membranes concerned, many of them
are roughly isotonic in this sense, and all may be considered isotonic across an ideal membrane.
Accordingly, the term isotonic is used with this meaning throughout the present chapter. Only a few
substances—those that penetrate animal membranes at a sufficient rate—will show exception to this
classification.
The remainder of this chapter is concerned with a discussion of isotonic solutions and the means by
which they can be buffered.
Measurement of TonicityThe tonicity of solutions can be determined by one of two methods. First, in the hemolytic method, the
effect of various solutions of the drug is observed on the appearance of red blood cells suspended in the
solutions. The various effects produced have been described in the previous section. Husa and his
associates27used this method. In their later work, a quantitative method developed by Hunter29 was
used based on the fact that a hypotonic solution liberates oxyhemoglobin in direct proportion to the
number of cells hemolyzed. By such means, the van't Hoff i factor can be determined and the value
compared with that computed from cryoscopic data, osmotic coefficient, and activity coefficient.30
Husa found that a drug having the proper i value as measured by freezing point depression or computed
from theoretical equations nevertheless may hemolyze human red blood cells; it was on this basis that
he suggested restriction of the term isotonic to solutions having equal osmotic pressures with respect to
a particular membrane.
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Table 8-3 Average Liso Values for Various Ionic Types*
TypeLisoExamples
Nonelectrolytes1.9Sucrose, glycerin, urea, camphor
Weak electrolytes2.0Boric acid, cocaine, phenobarbital
Di-divalent electrolytes
2.0Magnesium sulfate, zinc sulfate
Uni-univalent electrolytes
3.4Sodium chloride, cocaine hydrochloride, sodium phenobarbital
Uni-divalent electrolytes
4.3Sodium sulfate, atropine sulfate
Di-univalent electrolytes
4.8Zinc chloride, calcium bromide
Uni-trivalent electrolytes
5.2Sodium citrate, sodium phosphate
Tri-univalent electrolytes
6.0Aluminum chloride, ferric iodide
Tetraborate electrolytes
7.6Sodium borate, potassium borate
*From J. M. Wells, J. Am. Pharm. Assoc. Pract. Ed. 5, 99, 1944.
The second approach used to measure tonicity is based on any of the methods that determine
colligative properties earlier in the book. Goyan and Reck28investigated various modifications of the
Hill–Baldes technique31 for measuring tonicity. This method is based on a measurement of the slight
temperature differences arising from differences in the vapor pressure of thermally insulated samples
contained in constant-humidity chambers.
One of the first references to the determination of the freezing point of blood and tears (as was
necessary to make solutions isotonic with these fluids) is that of Lumiere and Chevrotier,32 in which the
values of -0.56°C and -0.80°C were given, respectively, for the two fluids. Following work by Pedersen-
Bjergaard and coworkers,33,34 however, it is now well established that -0.52°C is the freezing point of
both human blood and lacrimal fluid. This temperature corresponds to the freezing point of a 0.90%
NaCl solution, which is therefore considered to be isotonic with both blood and lacrimal fluid.
Calculating Tonicity Using Liso ValuesBecause the freezing point depressions for solutions of electrolytes of both the weak and strong types
are always greater than those calculated from the equation ΔTf= Kfc, a new factor, L = i Kf, is introduced
to overcome this difficulty.35 The equation, already discussed is
The L value can be obtained from the freezing point lowering of solutions of representative compounds
of a given ionic type at a concentration c that is isotonic with body fluids. This specific value of L is
written as Liso.
The Liso value for a 0.90% (0.154 M) solution of sodium chloride, which has a freezing point depression
of 0.52°C and is thus isotonic with body fluids, is 3.4: From
we have
The interionic attraction in solutions that are not too concentrated is roughly the same for all uni-
univalent electrolytes regardless of the chemical nature of the various compounds of this class, and all
have about the same value for Liso, namely 3.4. As a result of this similarity between compounds of a
given ionic type, a table can be arranged listing the L value for each class of electrolytes at a
concentration that is isotonic with body fluids. The Liso values obtained in this way are given in Table 8-3.
It will be observed that for dilute solutions of nonelectrolytes, Liso is approximately equal to Kf. Table 8-
3 is used to obtain the approximate ΔTf for a solution of a drug if the ionic type can be correctly
ascertained. A plot of i Kf against molar concentration of various types of electrolytes, from which the
values of Liso can be read, is shown in Figure 6-7 (in Chapter 6, “Electrolytes and Ionic Equilibria”).
Example 8-11Freezing Point LoweringWhat is the freezing point lowering of a 1% solution of sodium propionate (molecular weight 96)? Because sodium propionate is a uni-univalent electrolyte, its Liso value is 3.4. The molar concentration of a 1% solution of this compound is 0.104. We have
Although 1 g/100 mL of sodium propionate is not the isotonic concentration, it is still proper to use Liso as
a simple average that agrees with the concentration range expected for the finished solution. The
selection of L values in this concentration region is not sensitive to minor changes in concentration; no
pretense to accuracy greater than about 10% is implied or needed in these calculations.
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The calculation of Example 8-11 can be simplified by expressing molarity c as grams of drug contained
in a definite volume of solution. Thus,
or
where w is the grams of solute, MW is the molecular weight of the solute, and v is the volume of solution
in milliliters. Substituting in equation (8-36) gives
The problem in Example 8-11 can be solved in one operation by the use of equation (8-41) without the
added calculation needed to obtain the molar concentration:
The student is encouraged to derive expressions of this type; certainly equations (8-40) and (8-
41) should not be memorized, for they are not remembered for long. The Liso values can also be used for
calculating sodium chloride equivalents and Sprowls V values, as discussed in subsequent sections of
this chapter.
Methods of Adjusting Tonicity and pHOne of several methods can be used to calculate the quantity of sodium chloride, dextrose, and other
substances that may be added to solutions of drugs to render them isotonic.
For discussion purposes, the methods are divided into two classes. In the class I methods, sodium
chloride or some other substance is added to the solution of the drug to lower the freezing point of the
solution to -0.52°C and thus make it isotonic with body fluids. Under this class are included
the cryoscopic method and thesodium chloride equivalent method. In the class II methods, water is
added to the drug in a sufficient amount to form an isotonic solution. The preparation is then brought to
its final volume with an isotonic or a buffered isotonic dilution solution. Included in this class are
the White–Vincent method and the Sprowls method.
Class I MethodsCryoscopic MethodThe freezing point depressions of a number of drug solutions, determined experimentally or
theoretically, are given in Table 8-4. According to the previous section, the freezing point depressions of
drug solutions that have not been determined experimentally can be estimated from theoretical
considerations, knowing only the molecular weight of the drug and the Liso value of the ionic class.
The calculations involved in the cryoscopic method are explained best by an example.
Example 8-12IsotonicityHow much sodium chloride is required to render 100 mL of a 1% solution of apomorphine hydrochloride isotonic with blood serum?From Table 8-4 it is found that a 1% solution of the drug has a freezing point lowering of 0.08°C. To make this solution isotonic with blood, sufficient sodium chloride must be added to reduce the freezing point by an additional 0.44°C (0.52°C - 0.08°C). In the freezing point table, it is also observed that a 1% solution of sodium chloride has a freezing point lowering of 0.58°C. By the method of proportion,
Thus, 0.76% sodium chloride will lower the freezing point the required 0.44°C and will render the solution isotonic. The solution is prepared by dissolving 1.0 g of apomorphine hydrochloride and 0.76 g of sodium chloride in sufficient water to make 100 mL of solution.
Sodium Chloride Equivalent MethodA second method for adjusting the tonicity of pharmaceutical solutions was developed by Mellen and
Seltzer.36 The sodium chloride equivalent or, as referred to by these workers, the “tonicic equivalent” of
a drug is the amount of sodium chloride that is equivalent to (i.e., has the same osmotic effect as) 1 g,
or other weight unit, of the drug. The sodium chloride equivalents E for a number of drugs are listed
in Table 8-4.
When the E value for a new drug is desired for inclusion in Table 8-4, it can be calculated from
the Liso value or freezing point depression of the drug according to formulas derived by Goyan et
al.37 For a solution containing 1 g of drug in 1000 mL of solution, the concentration c expressed in
moles/liter can be written as
and from equation (8-36)
Now, E is the weight of NaCl with the same freezing point depression as 1 g of the drug, and for a NaCl
solution containing E grams of drug per 1000 mL,
where 3.4 is the Liso value for sodium chloride and 58.45 is its molecular weight. Equating these two
values of ΔTf yields
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Table 8-4 Isotonic Values*, †
SubstanceMWEVΔTf1%Liso
Alcohol, dehydrated46.070.7023.30.411.9
Aminophylline456.460.175.70.104.6
Amphetamine sulfate368.490.227.30.134.8
Antipyrine188.220.175.70.101.9
Apomorphine hydrochloride
312.790.144.70.082.6
Ascorbic acid176.120.186.00.111.9
Atropine sulfate694.820.134.30.075.3
Diphenhydramine hydrochloride
291.810.206.60.343.4
Boric acid61.840.5016.70.291.8
Caffeine194.190.082.70.050.9
Dextrose·H2O198.170.165.30.091.9
Ephedrine hydrochloride
201.690.3010.00.183.6
Ephedrine sulfate428.540.237.70.145.8
Epinephrine hydrochloride
219.660.299.70.173.7
Glycerin92.090.3411.30.201.8
Lactose360.310.072.30.041.7
Morphine hydrochloride
375.840.155.00.093.3
Morphine sulfate758.820.144.80.086.2
Neomycin sulfate–0.113.70.06–
Penicillin G potassium372.470.186.00.113.9
Penicillin G Procaine588.710.103.30.063.5
Phenobarbital sodium254.220.248.00.143.6
Phenol94.110.3511.70.201.9
Potassium chloride74.550.7625.30.453.3
Procaine hydrochloride
272.770.217.00.123.4
Quinine hydrochloride396.910.144.70.083.3
Sodium chloride58.451.0033.30.583.4
Streptomycin sulfate1457.440.072.30.046.0
Sucrose342.300.082.70.051.6
Tetracycline hydrochloride
480.920.144.70.084.0
Urea60.060.5919.70.352.1
Zinc chloride139.290.6220.30.375.1
*The values were obtained from the data of E. R. Hammarlund and K. Pedersen-Bjergaard, J. Am. Pharm. Assoc. Pract. Ed. 19, 39, 1958; J. Am. Pharm. Assoc. Sci. Ed. 47, 107, 1958; and other sources. The values vary somewhat with concentration, and those in the table are for 1% to 3% solutions of the drugs in most instances. A complete table of Eand ΔTf values is found in the Merck Index, 11th Ed., Merck, Rahway, N. J., 1989, pp. MISC-79 to MISC-103. For the most recent results of Hammarlund, see J. Pharm. Sci. 70, 1161, 1981; 78, 519, 1989.Key: MW = molecular weight of the drug; E = sodium chloride equivalent of the drug; V = volume in mL of isotonic solution that can be prepared by adding water to 0.3 g of the drug (the weight of drug in 1 fluid ounce of a 1% solution); ΔTf
1% = freezing point depression of a 1% solution of the drug; Liso = the molar freezing point depression of the drug at a concentration approximately isotonic with blood and lacrimal fluid.
†The full table is available at the book's companion website at thepoint.lww.com/Sinko6e.
Example 8-13Sodium Chloride Equivalents
Calculate the approximate E value for a new amphetamine hydrochloride derivative (molecular weight 187).Because this drug is a uni-univalent salt, it has an Liso value of 3.4. Its E value is calculated from equation (8-45):
Calculations for determining the amount of sodium chloride or other inert substance to render a solution
isotonic (across an ideal membrane) simply involve multiplying the quantity of each drug in the
prescription by its sodium chloride equivalent and subtracting this value from the concentration of
sodium chloride that is isotonic with body fluids, namely, 0.9 g/100 mL.
Example 8-14Tonicity AdjustmentA solution contains 1.0 g of ephedrine sulfate in a volume of 100 mL. What quantity of sodium chloride must be added to make the solution isotonic? How much dextrose would be required for this purpose?The quantity of the drug is multiplied by its sodium chloride equivalent, E, giving the weight of sodium chloride to which the quantity of drug is equivalent in osmotic pressure:
The ephedrine sulfate has contributed a weight of material osmotically equivalent to 0.23 g of sodium chloride. Because a total of 0.9 g of sodium chloride is required for isotonicity, 0.67 g (0.90 - 0.23 g) of NaCl must be added.If one desired to use dextrose instead of sodium chloride to adjust the tonicity, the quantity would be estimated by setting up the following proportion. Because the sodium chloride equivalent of dextrose is 0.16,
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Other agents than dextrose can of course be used to replace NaCl. It is recognized that thimerosal
becomes less stable in eye drops when a halogen salt is used as an “isotonic agent” (i.e., an agent like
NaCl ordinarily used to adjust the tonicity of a drug solution). Reader38 found that mannitol, propylene
glycol, or glycerin—isotonic agents that did not have a detrimental effect on the stability of thimerosal—
could serve as alternatives to sodium chloride. The concentration of these agents for isotonicity is
readily calculated by use of the equation (see Example 8-14)
where X is the grams of isotonic agent required to adjust the tonicity, Y is the additional amount of NaCl
for isotonicity over and above the osmotic equivalence of NaCl provided by the drugs in the solution,
and E is the sodium chloride equivalence of the isotonic agent.
Example 8-15Isotonic SolutionsLet us prepare 200 mL of an isotonic aqueous solution of thimerosal, molecular weight 404.84 g/mole. The concentration of this anti-infective drug is 1:5000, or 0.2 g/1000 mL. The Liso for such a compound, a salt of a weak acid and a strong base (a 1:1 electrolyte), is 3.4, and the sodium chloride equivalent E is
The quantity of thimerosal, 0.04 g for the 200-mL solution, multiplied by its E value gives the weight of NaCl to which the drug is osmotically equivalent:
Because the total amount of NaCl needed for isotonicity is 0.9 g/100 mL, or 1.8 g for the 200-mL solution, and because an equivalent of 0.0057 g of NaCl has been provided by the thimerosal, the additional amount of NaCl needed for isotonicity, Y, is
This is the additional amount of NaCl needed for isotonicity. The result, 1.8 g of NaCl, shows that the concentration of thimerosal is so small that it contributes almost nothing to the isotonicity of the solution. Thus, a concentration of 0.9% NaCl, or 1.8 g/200 mL, is required.However, from the work of Reader38 we know that sodium chloride interacts with mercury compounds such as thimerosal to reduce the stability and effectiveness of this preparation. Therefore, we replace NaCl with propylene glycol as the isotonic agent.From equation (8-45) we calculate the E value of propylene glycol, a nonelectrolyte with an Liso value of 1.9 and a molecular weight of 76.09 g/mole:
Using equation (8-46), X = Y/E, we obtain
where X = 4.3 g is the amount of propylene glycol required to adjust the 200-mL solution of thimerosal to isotonicity.
Class II MethodsWhite–Vincent MethodThe class II methods of computing tonicity involve the addition of water to the drugs to make an isotonic
solution, followed by the addition of an isotonic or isotonic-buffered diluting vehicle to bring the solution
to the final volume. Stimulated by the need to adjust the pH in addition to the tonicity of ophthalmic
solutions, White and Vincent39 developed a simplified method for such calculations. The derivation of
the equation is best shown as follows.
Suppose that one wishes to make 30 mL of a 1% solution of procaine hydrochloride isotonic with body
fluid. First, the weight of the drug, w, is multiplied by the sodium chloride equivalent, E:
This is the quantity of sodium chloride osmotically equivalent to 0.3 g of procaine hydrochloride.
Second, it is known that 0.9 g of sodium chloride, when dissolved in enough water to make 100 mL,
yields a solution that is isotonic. The volume, V, of isotonic solution that can be prepared from 0.063 g of
sodium chloride (equivalent to 0.3 g of procaine hydrochloride) is obtained by solving the proportion
In equation (8-49), the quantity 0.063 is equal to the weight of drug, w, multiplied by the sodium chloride
equivalent, E, as seen in equation (8-47). The value of the ratio 100/0.9 is 111.1. Accordingly,
equation (8-49) can be written as
where V is the volume in milliliters of isotonic solution that may be prepared by mixing the drug with
water, w is the weight in grams of the drug given in the problem, and E is the sodium chloride equivalent
obtained from Table 8-4. The constant, 111.1, represents the volume in milliliters of isotonic solution
obtained by dissolving 1 g of sodium chloride in water.
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The problem can be solved in one step using equation (8-51):
To complete the isotonic solution, enough isotonic sodium chloride solution, another isotonic solution, or
an isotonic-buffered diluting solution is added to make 30 mL of the finished product.
When more than one ingredient is contained in an isotonic preparation, the volumes of isotonic solution,
obtained by mixing each drug with water, are additive.
Example 8-16Isotonic SolutionsMake the following solution isotonic with respect to an ideal membrane:
The drugs are mixed with water to make 18 mL of an isotonic solution, and the preparation is brought to a volume of 100 mL by adding an isotonic diluting solution.
The Sprowls MethodA further simplification of the method of White and Vincent was introduced by Sprowls.40 He recognized
that equation (8-51) could be used to construct a table of values of V when the weight of the drug, w,
was arbitrarily fixed. Sprowls chose as the weight of drug 0.3 g, the quantity for 1 fluid ounce of a 1%
solution. The volume,V, of isotonic solution that can be prepared by mixing 0.3 g of a drug with sufficient
water can be computed for drugs commonly used in ophthalmic and parenteral solutions. The method
as described by Sprowls40 is further discussed in several reports by Martin and Sprowls.41 The table
can be found in the United States Pharmacopeia. A modification of the original table was made by
Hammarlund and Pedersen-Bjergaard42 and the values of V are given in column 4 of Table 8-4, where
the volume in milliliters of isotonic solution for 0.3 g of the drug, the quantity for 1 fluid ounce of a 1%
solution, is listed. (The volume of isotonic solution in milliliters for 1 g of the drug can also be listed in
tabular form if desired by multiplying the values in column 4 by 3.3.) The primary quantity of isotonic
solution is finally brought to the specified volume with the desired isotonic or isotonic-buffered diluting
solutions.
Chapter SummaryBuffers are compounds or mixtures of compounds that, by their presence in solution, resist changes in pH upon the addition of small quantities of acid or alkali. The resistance to a change in pH is known as buffer action. If a small amount of a strong acid or base is added to water or a solution of sodium chloride, the pH is altered considerably; such systems have no buffer action. In this chapter, the theory of buffers was introduced as were several formulas for making commonly used buffers. Finally, the important concept of tonicity was introduced. Pharmaceutical buffers must usually be made isotonic so that they cause no swelling or contraction of biological tissues, which would lead to discomfort in the patient being treated.Practice problems for this chapter can be found at thePoint.lww.com/Sinko6e.
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Recommended ReadingsR. J. Benyon, Buffer Solutions (The Basics), BIOS Scientific Publishers, Oxford, UK, 1996.
Chapter LegacyFifth Edition: published as Chapter 9 (Buffered and Isotonic Solutions). Updated by Patrick Sinko.Sixth Edition: published as Chapter 8 (Buffered and Isotonic Solutions). Updated by Patrick Sinko.
